Question:
(a) How many sub-shells are associated with n = 4?
(b) How many electrons will be present in the sub-shells having $m_{s}$ value of $-1 / 2$ for $n=4 ?$
Solution:
(a) $n=4$ (Given)
For a given value of ' $n$ ', ' $r$ can have values from zero to $(n-1)$.
$\therefore I=0,1,2,3$
Thus, four sub-shells are associated with n = 4, which are s, p, d and f.
(b) Number of orbitals in the $n^{\text {th }}$ shell $=n^{2}$
For $n=4$
Number of orbitals = 16
If each orbital is taken fully, then it will have 1 electron with $m_{s}$ value of $-\frac{1}{2}$.
$\therefore$ Number of electrons with $m_{s}$ value of $\left(-\frac{1}{2}\right)$ is 16 .